1. Suppose that based on data obtained from a hypothetical social survey on COVID-19 vacci- nation among the US adults we obtained the following equations. The response variable is vaccination status with three different categories, will not get a vaccine (WNG), will get a vaccine (WG), have already received at least one dose of vaccine (G). The covariates in the study are 1) race with three categories black (B), hispanic (H) , white (W), 2) income with three categories high (H), middle (M), low (L), and 3) gender with two categories female (F) and male (M). TT G log = 1 + 0.41(race = H) + 0.31(race = W) + 0.11(gender = M) TWNG -0.41(income = L) - 0.21(income = M), TWG log 1.25 + 0.21(race = H) + 0.281(race = W) + 0.181(gender = M) TWNG -0.251(income = L) - 0.151(income = M). Here I denotes the indicator function, and TG, TWNG and TWG are the probabilities for three categories of the response variable. (a) Obtain the prediction equation for log("G/TWG). [5] (b) Obtain the numeric values of TG, TWNG and TWG for white male in the low income group. Report the results upto three decimal places. [5]